The circle in an axonometry represents an ellipse. It is possible to construct it by means of parallel projection of a circle of the set radius on the plane.
It is required to you
- - paper;
- - ruler;
- - pencil;
- - eraser;
- - triangle with a right angle;
- - compasses;
- - protractor.
Instruction
1. To draw an ellipse in an axonometry, at first it is necessary to construct ABCD parallelogram. In the turned-out parallelogram it is necessary to carry out diagonals. For this purpose connect points of A and C, B and D. Receive diagonals of AC and BD. Designate a point of their crossing by letter O.
2. Note the middle of the parties of a parallelogram points 1, 3, 5, 7. You can just halve lengths of the parties and note the middle. Or you can apply a ruler to the party of a parallelogram of AB and its message parallel to AB before crossing with O. Ostanovite's point a ruler and note on sides of a parallelogram of AD and BC of a point 1 and 5. Then repeat the same procedure and note the middle of the top and bottom side of a parallelogram points 3 and 7.
3. On a piece 3B construct down an isosceles rectangular triangle of 3KB where 3B is a triangle hypotenuse. By means of a protractor measure a corner in 45 ° about a point 3 down and to the right. Then note 45 ° from B point down and to the left. Draw straight lines on noted corners. A point of their crossing - top of a right angle of K.
4. Take compasses and carry out a semi-circle from a point 3 with a radius of 3K before crossing with the party of a parallelogram of AB. Points of intersection designate L and M. These points divide a piece 3A and equal to it 3B concerning 3:7. If you have no compasses, try to divide half of the party of AB in the ratio 3:7 by means of a ruler, but it reduces construction accuracy.
5. Draw through points L and M straight lines parallel to sides of AD and BC before crossing with parallelogram diagonals. Note points 2, 4, 6, 8.
6. Construct in points the 2 and 6 tangents of t ₂ and t ₆ parallel diagonals of BD and in points the 4 and 8 tangents of t ₄ and t ₈ parallel diagonals of AC. They will be tangents to an ellipse in points 2, 4, 6 and 8.
7. At you it turned out to construct 8 points of an ellipse 1, 2, 3, 4, 5, 6, 7 and 8 and as much tangents to an ellipse of AD, t ₂, AB, t ₄, BC, t ₆, CD and t ₈. Now you can with a sufficient accuracy draw in a parallelogram an ellipse. At first draw a weak contour, then circle an ellipse with the thick line.